A free-stepsize implementation of second order stable methods for neutral delay differential equations

摘要

The approach is based on viewing the DDE as an ODE with forcing term and naturally extends to any kind of delay τ, even “state-dependent" τ = τ(t,y(t)). The same arguments used for the stability analysis of the solution y(t) apply to the numerical approximation η(t) and allow to select some second order continuous ODE-methods which preserve the asymptotic stability for any constant integration stepsize. A prominent method in this class is the two-stage Lobatto III-C method with linear interpolation (see Bellen and Zennaro [2]).